The analysis of raft is carried out in SAFE software. The mat is provided with an offset of 0.5 m from face of the column. he vertical loads and moments on the column are transferred on the mat as column reaction load. Then the mat is analyzed for various parameters.
Raft is divided into three strips A, B and C. Different thicknesses of the raft (0.5m to 1.5m) and for various Modulus of subgrade reactions (5000, to 25000 KN/m3) has been used. Results of deflection are checked for various load combinations and worst load combination is identified and used for further analysis.
4.1 Relative stiffness
In the conventional design practice, building frames are generally considered to be fixed at their bases. But in reality, soil support is slightly flexible which allows some movement of foundation. This decreases the overall stiffness of the building frames in connection with soil and in turn overall response of building and or foundation is altered [6].
The flexural rigidities of super structure and foundation elements and stiffness’s of soil has been identified as indices for defining parameters which assist in the interpretation of the soil – foundation – structure interaction results. For the study purpose following equation (i) is considered in line with IS:2950 part I 1981 [1].
where Kr < 0.5: Flexible and Kr ≥ 0.5: Rigid
Flexible analysis carried out through computer programs for mat foundations is usually based on an approximation. In this case mat is divided into a number of discrete (finite) elements using grid lines. FGM and FEM techniques are useful when mats have curved boundaries All methods use the modulus of subgrade reaction k, as the soil contribution to the structural model. Computers software makes the use of any of the discrete element methods economical and rapid [19].
Even though the contact pressure distribution is not uniform at base of rigid footing, any point at base of footing settles through same amount. Hence for rigorous methods, as the contact pressure distribution is complicated, it is assumed that settlement of point is independent of size of area and of the load acts [9].
For long beams Vesic (1961) proposed an equation (ii) for estimation of sub grade reaction that can be expressed as
where,
k = modulus of sub grade reaction, Es = modulus of elasticity of soil, µs = Poisson’s ratio of soil
In recent revision of IS 2950 (part-I) 1981, conventional and flexible method are suggested for design of raft foundation. In conventional method regular planer contact pressure is considered which is not possible under dynamic loading. In case of flexible raft, simplified (similar to soil line method) method has been suggested. When column loads are varying more than 20% elastic plate load theory has been suggested. Code also says that
- The effect of size and shape of raft on subgrade modulus must be taken in to consideration.
- The increased contact pressure at the edge of raft on cohesive and opposite effect on non-cohesive soil need to be incorporated.
But the code dose not explicitly provides any guidance about how to utilize these factors. There has not been any further revision and this code was reaffirmed in 1987. In practice, however, raft is analyzed as per guidelines of codes for gravity loading which do not completely simulate the field conditions. The most of the research is focused on soil structure interaction and flexible analysis of raft. From the literature review and IS code provision focus more on static loading conditions. A more comprehensive study of seismic/dynamic analysis of rafts is needed so that a satisfactory solution for the analysis of raft foundations under seismic forces can be determined.
4.2 Relative Stiffness Factor
Table1: Relative stiffness for varying soil modulus and raft stiffness
K in kN/m2/m
|
Thickness of raft
|
0.5m
|
1.0m
|
1.5m
|
5000
|
0.28 (F)
|
2.25 (R)
|
7.61 (R)
|
10000
|
0.14 (F)
|
1.13 (R)
|
3.81 (R)
|
25000
|
0.06 (F)
|
0.45 (F)
|
1.52 (R)
|
Where, F- Flexible Raft, R-Rigid Raft.